Autumn 2019 Ling 5201 Syntax I 3: Basic clause structure Robert Levine Ohio State University levine.1@osu.edu Robert Levine 2019 5201 1 / 30
Where we left off. . . ◮ What we have: mary ; m ; NP (1) john ; j ; NP criticized ; criticize ; ( NP \ S ) / NP ◮ What we want. . . john ; j ; NP criticized ; criticize ; ( NP \ S ) / NP (2) criticized • john ; criticize ( j ) ; ( NP \ S ) mary ; m ; NP mary • criticized • john ; criticize ( j )( m ) ; S ◮ . . . So how are we going to get it? Robert Levine 2019 5201 2 / 30
A first attempt: the AB gramar ◮ Here’s what I propose: / Elim \ Elim b ; P ; B/A a ; α ; A b ; P ; A \ B a ; α ; A b • a ; P ( α ) ; B a • b ; P ( α ) ; B ◮ The logic of the types drives the whole proof: ◮ A \ B and B/A are both implications: ‘give me an A and I’ll give you back a B. ◮ The A-type term is given (i.e., either already proven or lexically listed), ◮ and the result is a B-type object. ◮ The semantics applies the denotation labeling the implication to the semantics of the antecedent premise ( α ), ◮ and the prosody is the concatenation of the implication term and the antecedent term in an order determined by the direction of the implication. Robert Levine 2019 5201 3 / 30
Applying the rules / E(lim) \ E(lim) b ; P ; B/A a ; α ; A b ; P ; A \ B a ; α ; A b • a ; P ( α ) ; B a • b ; P ( α ) ; B (3) john ; j ; NP criticized ; criticize ; ( NP \ S ) / NP / E criticized • john ; criticize ( j ) ; ( NP \ S ) mary ; m ; NP \ E mary • criticized • john ; criticize ( j )( m ) ; S Robert Levine 2019 5201 4 / 30
The semantic part. . . ◮ So our analysis of Mary criticized John derives a meaning we write as criticize ( j )( m ) . ◮ But what does this expression really denote? What is it supposed to tell us? ◮ The most influential view of semantics for the past half century, originating in the work of Richard Montague, is that ◮ a semantic representation of a sentence S is an explicit statement of the truth conditions on sentences ◮ formulated in terms of a set-theoretic model ◮ that corresponds in 1-to-1 fashion with how the world is structured. ◮ That view entails that the truth of a sentence must be evaluated with respect to a specific set-theoretic model, ◮ since different models correspond to different possible ways the world could be, ◮ or, for short, different ‘possible worlds’. Robert Levine 2019 5201 5 / 30
More on semantics. . . ◮ To see how these general ideas can be used as a tool to match form and meaning, ◮ let’s take something a little simpler to start with: (4) John walks. ◮ This will be true just in case ◮ there is some object in our mathematical analogue of the world—call it j — ◮ who is a member of a certain set, whose name is walk . ◮ Or, in more compact form, j ∈ walk . ◮ Now, in terms of our inference rules, this analysis appears to present a problem: walks ; walk ; NP \ S john ; j ; NP (5) john • walks ; walk ( j ) ; S ◮ What is the problem here?? Robert Levine 2019 5201 6 / 30
Still more on semantics. . . ◮ The problem is that a set is a set, not a function. ◮ It doesn’t take arguments. ◮ This looks like a big problem for our analysis, ◮ because, for reasons of generality, we need the semantics to correspond in general to a function applied to an argument. ◮ So are we in trouble here? Is there a way out? Robert Levine 2019 5201 7 / 30
And still more on semantics. . . ◮ We can model a set as a function. ◮ So we have (6) { j , m , a } ◮ Suppose we have a function which returns 1 for j,m, and a and 0 for everything else. j → 1 → s 0 b → 0 → r 0 → a 1 k → 0 → m 1 . . . . . . Robert Levine 2019 5201 8 / 30
And still more on semantics. . . ◮ There is a 1-to-1 relationship between such a function and the values that the set whose members are mapped to 0 by that function, ◮ which means that we can in effect interpret the meaning of walks to be either ‘static’ (as a set) or ‘dynamic’ (as a function) depending on the work we need this meaning to do. ◮ The two ways of interpreting this meaning are in effect the two sides of a single semantic coin. ◮ With much in hand, we can work out the interpretations required for more complex syntactic objects. Robert Levine 2019 5201 9 / 30
Transitive verbs ◮ For example: our transitive verb criticize . ◮ We know that criticized John corresopnds to a function which, exactly like walks , picks up an NP on its left to yield an S. ◮ The semantics are exactly parallel too: criticized John denotes a set, ◮ and Mary criticized John is true just in case Mary is a member of that set. ◮ So once we have criticized John , we know we have a function from individuals to the truth values 1 or 0 . ◮ But how did we get criticized John ? Robert Levine 2019 5201 10 / 30
More on transitive verbs ◮ Since, by our proof, criticized combines with John to get criticized John , ◮ and since criticized John denotes a property (a set, or the function corresponding to that set), ◮ it follows that criticized corresponds to a function which ◮ semantically combines with an individual (corresponding to e.g. j ), ◮ returns a pronunciation criticized • john , and ◮ and a matching interpretation as a property, criticize ( j ) . ◮ Thus the semantic difference between an intransitive verb such as walks and an intransitive verb like criticized is the difference between ◮ a property on the one hand ◮ and a function from an individual to a property on the other. Robert Levine 2019 5201 11 / 30
Summing up Expression kind Syntactic type Semantic kind Semantic type sentence S truth value ( { 1 , 0 } ) t noun phrase NP individual ( m , j , b , a . . . ) e intransitive verb NP \ S property ( walks , slept , eating . . . ) � e, t � transitive verb ( NP \ S ) / NP relation ( sees , criticizes , eating . . . ) � e, � e, t �� ◮ This table can be extended considerably; so we have verbs that combine ◮ with two NPs to yield a VP ( sent Mary a book , ◮ with an NP and a PP ( sent a book to Mary ), ◮ with two NPs and a PP ( bet John ten dollars on the outcome ) ◮ and so on and on. ◮ The key point is that the syntactic type and the semantic type match perfectly, in that ◮ given a syntactic type, we can identify the corresponding semantic type uniquely. Robert Levine 2019 5201 12 / 30
◮ This outcome makes complete sense in terms of the higher order logic we are assuming as the compositional ‘engine’ of our framework, ◮ in that, in HOL, logical connectives such as implication, conjunction, negation etc. are considered to be functions . ◮ Thus, the logical formula p ⊃ q is regarded as a function which takes the truth values of propositiona p, q to a third truth value, ◮ so of type � t, � t, t �� . ◮ We aren’t thinking of implication in terms of truth, of course. . . ◮ but rather, syntactic composition. ◮ So the implicational connectives /, \ for us are functions which take syntactic types to other syntactic types; ◮ e.g., criticize is a function of syntactic type � NP, � NP, S �� ◮ and semantic type � e, � e, t �� . ◮ which is just what you get replacing NP with its semantic type e and S with its syntactic type t , ◮ illustrating why we refer to types of the form X \ Y or Y / X as functional types . Robert Levine 2019 5201 13 / 30
Adjuncts vs. complements ◮ Some parts of sentences depend on lexical properties: (7) a. I told John to leave b. I told John that he had to leave. (8) a. told ; tell ; (( NP \ S ) / VP [ inf ]) / NP b. told ; tell ; (( NP \ S ) / S [ that ]) / NP (9) a. *I informed John to leave. b. I informed John that he had to leave. (10) informed ; inform ; ( NP \ S ) / S [ that ] (11) a. I ordered John to leave. b. *I ordered John that he had to leave. (12) ordered ; order ; (( NP \ S ) / VP [ inf ]) / NP Robert Levine 2019 5201 14 / 30
◮ . . . and some DON’T : 8 reflected 9 > > read the book > > > > > > > > > showed the evidence to John > > > > > > > showed John the evidence > > > > > > > > told John to leave < = (13) Mary quietly told John that he had to leave > > > > ordered John to leave > > > > > > > > informed John that he had to leave > > > > > > > > . > > > > . > > : . ; ◮ What do we want to say about quietly here? ◮ How shall we say it? ◮ Suppose we say (14) quietly ; quietly ; ( NP \ S ) / ( NP \ S ) Robert Levine 2019 5201 15 / 30
◮ Then the following proof is legal: read ; the • book ; read ; ( NP \ S ) / NP the-book ; NP / E read • the • book ; quietly ; read ( the-book ); quietly ; NP \ S ( NP \ S ) / ( NP \ S ) / E quietly • read • the • book ; quietly ( read ( the-book )); mary ; NP \ S m ; NP \ E mary • quietly • read • the • book ; quietly ( read ( the-book ))( m ); S Robert Levine 2019 5201 16 / 30
◮ Since ( NP \ S ) / ( NP \ S ) is a functional type taking NP \ S as argument, ◮ its semantics is a function taking the semantics of read the book as argument. ◮ What work does this function do? ◮ Mary read the book must be true if Mary quietly read the book is true; i.e., ◮ if m ∈ quietly ( read ( the-book )) then necessarily m ∈ ( read ( the-book )) . . . ◮ but the converse does not hold. ◮ So what is the relationship between the two sets? Robert Levine 2019 5201 17 / 30
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